where \(g:\mathbb {R}^m\times \mathbb {R}^n \rightarrow \overline{\mathbb {R}}= [-\infty ,\infty ]\)  describes a quantity of interest depending on an \(n\) -dimensional decision vector \(x\)  and an \(m\) -dimensional random vector \(\mbox{$\xi $}\)  with probability distribution \(P\) . (We express random quantities using boldface letters and return to a regular font for their realizations.) As long as \(g(\cdot ,x)\)  is measurable for all \(x\) , the expectation function is well defined but possible not finite [1]} under the usual conventions of extended real-valued arithmetic which we assume throughoutMost significantly, \(0\cdot \infty = 0\)  and \(\infty - \infty =\infty \) ; see [1]}..
